Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Key Formulae

[exp(a)¼eafor any numbera]

LOGISTIC FUNCTION:f(z)¼1/[1þ exp(z)]

LOGISTIC MODEL: P(X)¼1/{1þexp[(aþ~biXi)]}

LOGIT TRANSFORMATION: logit P(X)¼aþ~biXi

RISK ODDS RATIO (general formula):

RORX 1 ;X 0 :¼exp½~biðX 1 iX 0 iފ¼Pfexp½biðX 1 iX 0 iފg

RISK ODDS RATIO [(0, 1) variables]: ROR¼exp(bi)

for the effect of the variableXiadjusted for the otherXs

Practice Exercises

Suppose you are interested in describing whether social

status, as measured by a (0, 1) variable called SOC, is

associated with cardiovascular disease mortality, as

defined by a (0, 1) variable called CVD. Suppose further

that you have carried out a 12-year follow-up study of 200

men who are 60 years old or older. In assessing the rela-

tionship between SOC and CVD, you decide that you want

to control for smoking status [SMK, a (0, 1) variable] and

systolic blood pressure (SBP, a continuous variable).

In analyzing your data, you decide to fit two logistic mod-

els, each involving the dependent variable CVD, but with

different sets of independent variables. The variables

involved in each model and their estimated coefficients

are listed below:

Model 1 Model 2

VARIABLE COEFFICIENT VARIABLE COEFFICIENT

CONSTANT 1.1800 CONSTANT 1.1900

SOC 0.5200 SOC 0.5000

SBP 0.0400 SBP 0.0100

SMK 0.5600 SMK 0.4200

SOCSBP 0.0330

SOCSMK 0.1750

1. For each of the models fitted above, state the form of the
   logistic model that was used (i.e., state the model in
   terms of the unknown population parameters and the
   independent variables being considered).

32 1. Introduction to Logistic Regression